Han Solo was going to marry Leia, and you look back and say, 'Should he be a cold-blooded killer?' Because I was thinking mythologically -- should he be a cowboy, should he be John Wayne? And I said, 'Yeah, he should be John Wayne.' And when you're John Wayne, you don't shoot people [first] -- you let them have the first shot. It's a mythological reality that we hope our society pays attention to.

In the 1997 "Special Edition" of Star Wars, Lucas edited the scene so that Greedo fires at Han first and then Han shoots him. In a 2004 edition of the film (the version that is currently available for download online), they fire at the same time. Lucas, however, has argued that the special edition was his original intent, stating in 2002:

The controversy over who shot first, Greedo or Han Solo, in Episode IV, what I did was try to clean up the confusion, but obviously it upset people because they wanted Solo to be a cold-blooded killer, but he actually isn't. It had been done in all close-ups and it was confusing about who did what to whom. I put a little wider shot in there that made it clear that Greedo is the one who shot first, but everyone wanted to think that Han shot first, because they wanted to think that he actually just gunned him down.

Reader Joshua W. thought that I had addressed this legend before, but I have not, but, well, here it is now, Joshua! Did Han originally shoot first or what?Here is the scene from the January 1976 version of the screenplay:

As Han is about to leave, Greedo, a slimy green-faced alien with a short trunk-nose, pokes a gun in his side. The creature speaks in a foreign tongue translated into English subtitles.GREEDOGoing somewhere, Solo?HANYes, Greedo. As a matter of fact,I was just going to see your boss.Tell Jabba that I've got his money.Han sits down and the alien sits across from him holding the gun on him.GREEDOIt's too late. You should havepaid him when you had the chance.Jabba's put a price on your head,so large that every bounty hunterin the galaxy will be looking foryou. I'm lucky I found you first.HANYeah, but this time I got the money.GREEDOIf you give it to me, I might forgetI found you.HANI don't have it with me. TellJabba...GREEDOJabba's through with you. He hasno time for smugglers who droptheir shipments at the first signof an Imperial cruiser.HANEven I get boarded sometimes. Doyou think I had a choice?Han Solo slowly reaches for his gun under the table.GREEDOYou can tell that to Jabba. Hemay only take your ship.HANOver my dead body.GREEDOThat's the idea I've been lookingforward to killing you for a longtime.HANYes, I'll bet you have.Suddenly the slimy alien disappears in a blinding flash of light. Han pulls his smoking gun from beneath the table as the other patrons look on in bemused amazement. Han gets up and starts out of the cantina, flipping the bartender some coins as he leaves.HANSorry about the mess.

That clears that up. Even if you wish to argue that when it actually came down to filming the scene in question, that Lucas somehow changed things up and felt that Han did not fire first, A. that isn't evident on the screen, as the film sure seems to show what Lucas wrote in the above script exactly and B. it wouldn't change the fact that Lucas originally did want Han Solo to shoot first, which is what he has since claimed he never believed in, because of his future plans for the character. There was one later edit of that screenplay in March 1976 before they began filming, but the Greedo scene remained the same. The legend is...STATUS: False